The following theorem extends and restricts Theorem 4.1 in [1]}. It makes an additional assumption of strand symmetry, but in so doing is able to accommodate rooted topologies. Motivated by Remark 4 in [1]}, it relaxes the assumption that every edge must be reconstructible from rows. Theorem 4.1 in [1]} allows degenerate topologies, where nodes are allowed to have degree greater than three. We assume nondegenerate topologies for ease of exposition and because we will only make that assumption later anyway when we prove that the model can be statistically consistently estimated, as Chang does in his Theorem 5.1. We note that extension of the following theorem to degenerate topologies should be straightforward.
